Extending the range of spectrally controlled interferometry by superposition of multiple spectral modulations

ABSTRACT

The range of measurement in spectrally controlled interferometry (SCI) is extended by superimposing multiple modulations on the low-coherence light used for the measurement. Optimally, a spectrally controllable light source modulated sinusoidally with low spectral frequency is combined with a delay line, such as provided by a Michelson interferometer. The resulting light is injected into a Fizeau interferometer to generate localized fringes at a distance corresponding to the effect of the spectrally modulated source combined with the optical path difference produced by the delay line. The combination provides a convenient way to practice SCI with all its advantages and with a range that can be extended to the degree required for any practically foreseeable application.

RELATED APPLICATIONS

This application is based on and claims the priority of U.S. ProvisionalApplication No. 62/427,959, filed on Nov. 30, 2016.

BACKGROUND OF THE INVENTION Field of the Invention

This invention relates in general to the field of interferometry and, inparticular, to a method and apparatus for extending the range ofspectrally controlled interferometry.

Description of the Prior Art

Spectrally controlled interferometry (SCI) is an interferometrictechnique that allows implementation of white light interferometry (WLI)measurement schemes in common-path interferometers. WLI is characterizedby the absence of coherent noise because of the light's short coherencelength, typically on the order of a few micrometers. However, WLIrequires careful balancing of the optical path difference (OPD) in theinterferometer so interference can take place in the measurement space(localized interference). Such arrangements can be complex and precludethe use of common-path interferometers, therefore forfeiting theadvantages of WLI.

Conventional laser interferometers have the problem that dust and othercontamination, diffraction on rough surfaces, etc., cause reducedmeasurement accuracy. Nonetheless, laser interferometry is extremelypopular because it allows the use of common-path interferometerdesigns—a particular class of devices in which most of the errorsintroduced by the optical system cancel out allowing the manufacture ofless expensive and more accurate instruments. The most commonly useddesign is the Fizeau interferometer.

SCI was introduced to the art during the last decade (see U.S. Pat. No.8,422,026) as a novel interferometric technique that successfullycombines both approaches and provides the advantages of both common-pathinterferometry and WLI. It produces localized interference in anunbalanced OPD interferometer along with means to introduce the phaseshift required to use modern fringe analysis methods. One of the majoradvantages of SCI is that existing instrumentation can be adapted tothis modality by replacing only the laser light source with one capableof proper spectral modulation. It allows the use, for example, of aFizeau interferometer in the WLI mode while eliminating the problem ofcoherent noise. A number of different interferometric techniques arepossible by manipulating only the spectral properties of such lightsource, as disclosed in co-owned U.S. Pat. No. 8,675,205, U.S. Pat. No.8,810,884, U.S. Pat. No. 9,581,428, U.S. Pat. No. 9,581,437, and U.S.Pat. No. 9,618,320. In many cases SCI can supplant conventional phaseshifting interferometry (PSI) because of its ability to isolate measuredsurfaces, directly measure distance from the reference object, andenable the performance of PSI without the use of any mechanical scanningmechanism.

However, practical interferometry applications often require thatfringes be formed at a large distance from the reference surface,sometimes as far as several meters, such as for measuring radius ofcurvature, astronomy mirrors, and large geometry systems. This isdifficult to achieve by spectral modulation alone because it requiresperiods of spectral modulation of the source on the order of picometersand shorter, which are difficult to achieve. Equation 1 expressesdistance L of fringe formation from the reference surface as a functionof the period Δλ of the spectral modulation for a source with meanwavelength λ:

$\begin{matrix}{{\Delta \; \lambda} = \frac{\lambda^{2}}{2L}} & (1)\end{matrix}$

For example, to form fringes at a distance of 1 m from the referencemirror for a source operating at a mean wavelength of 500 nm, the periodof modulation needs to be 0.125 pm. Such small modulation periods aredifficult both to produce and adequately control. Therefore, it would bevery desirable and advantageous to have a system that allows fringes toform at significant distances from the reference in common pathinterferometric configurations and that at the same time affords all theadvantages of SCI. This invention combines a spectrally modulated sourcewith an optical delay line to achieve this goal.

SUMMARY OF THE INVENTION

In a general sense, the invention lies in the recognition that, due tothe spectral modulation necessarily associated with spectrallycontrolled interferometry, the range of measurement space of theinterferometer can be extended by superimposing multiple modulations onthe low-coherence light used for the measurement. Optimally, theinterferometer is of common-path configuration and each modulation issinusoidal.

Accordingly, the preferred embodiment of the invention is thecombination of a spectrally controllable light source modulated with lowspectral frequency with a delay line, such as provided by a Michelsoninterferometer. The resulting light is capable of generating localizedfringes at a distance corresponding to the effect of the spectrallymodulated source combined with the optical path difference produced bythe delay line. Thus, the combination provides a convenient way topractice SCI with all its advantages and with a range that can beextended to the degree required for any practically foreseeableapplication.

Because the spectrally controllable source required for the broad rangeof applications afforded by SCI is capable of modulating frequency aswell as phase and amplitude of the spectrum, the invention enables thepractice of SCI for the same applications, without limitation, but witha range of measurement limited only by the geometry of the delay line ofthe second modulator. On the other hand, because the second modulator isrequired only to extend the range of measurement, which is defined bythe adopted period of modulation, the second modulator only needs to becapable of spectral modulation with adequately high frequency butwithout the need for the capability of controlling the modulation phase.

Various other advantages will become clear from the description of theinvention in the specification that follows and from the novel featuresparticularly pointed out in the appended claims. Therefore, thisinvention includes the features hereinafter illustrated in the drawings,fully described in the detailed description of the preferred embodimentsand particularly pointed out in the claims, but such drawings anddescription disclose only some of the various ways in which theinvention may be practiced.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of the components required topractice SCI with an extended measurement range according to theinvention.

FIG. 2 is a schematic illustration of the delay line portion of aconventional Michelson interferometer.

FIG. 3 presents three graphs illustrating the effect of superimposingtwo consecutive modulations on a source beam to produce fringe locationsover an extended range of measurement using SCI techniques.

FIG. 4 illustrates an SCI system configured to practice the invention.

DETAILED DESCRIPTION OF THE INVENTION

As used herein, “localized fringes” is intended to mean, in the case oflow-coherence light sources, interference fringes formed in a limitedspace around the location where the optical path difference (OPD)between the test and reference beams is close to zero; i.e., where thedelay between the reference and test beams is very small. In the case ofspectrally-controlled or multiple-wavelength sources, “localizedfringes” is intended to mean unambiguously identifiable fringe patternsformed at predetermined distances from the reference surface. Throughoutthis disclosure, the word “localized” and related terms are used forconvenience to describe the position of interferometric fringes in spacein relation to the reference mirror of the interferometer, but it isunderstood that such fringes are only virtual fringes and that actualfringes are in fact formed on the instrument's detector only when thetest surface is located at such “localized” positions in space.

Furthermore, as used in this disclosure, “white light” is intended torefer to any broadband light of the type used in the art of white-lightinterferometry, typically having a bandwidth on the order of manynanometers. Such bandwidth may be continuous or amount to a set ofdiscrete wavelengths over the bandwidth. With reference to light, theterms “frequency” and “wavelength” may be used alternatively, ascommonly done in the art, because of their well-known inverserelationship. “OPD” and “time delay” (τ) are used alternatively becauseof their space/time relationship in interferometry. The terms “modulate”and “modulation” in connection with a light source are meant in thebroadest sense as including any alteration of the frequencydistribution, amplitude distribution or phase distribution of energyproduced by the light source, and the synthesis of a light signal havinga desired frequency, amplitude and phase distribution by any means. Whenused in connection with interference fringes, the term “modulation”refers to the fringe envelope. As specified above, localized fringes aredescribed as positioned at the surfaces from which they are produced toillustrate how they relate to those surfaces and surface shapes thatproduce them; however, it is to be understood that physically thelocalized fringes actually exist in measurement space at the surface ofa detector. Also, the phrase “producing localized fringes at apredetermined position in space” and related expressions are used forconvenience, but it is understood that the precise intended meaning is“producing an interferometric environment whereby unambiguouslyidentifiable fringe patterns are produced when a test surface is placeat a predetermined position in space” relative to a reference surface.The terms “fringes” and “fringe patterns” are used interchangeablywithin the meaning normally accorded to them in the art. Finally, thegeneric term “interferometry” and related terms should be construedbroadly as used in the art and not limited to shape measurements usingan imaging interferometer. As such, interferometry is intended toinclude, without limitation, the measurement of changes in the positionof an object, or of thickness of optical elements, using any knowninterferometric technique.

As mentioned, the present invention lies in the combination of aspectrally controllable light source, such as described in U.S. Pat. No.8,810,884, with an additional spectrum modulator, such as a delay line,that introduces further frequency modulation in the light produced bythe spectrally controllable source. The resulting beam is then injectedinto an interferometer, preferably a common-path interferometer, topractice SCI with a measurement range that can be extended simply bycontrolling the modulation produced by the delay line (for example).Referring to the drawings, FIG. 1 represents schematically an SCI systemaccording to the invention. It includes a spectrally controllablesource, which generally consists of a broadband light source S and afirst spectrum modulator M₁ that applies a preferably sinusoidalmodulation to the spectrum emitted by the source S; a second spectrummodulator M₂, and an interferometer I. The period of modulation Δλ₁ ofthe spectrally controllable source is preferably chosen such thatinterferometric fringes are formed at a short distance from thereference surface. This is because it is relatively easy in practice toimplement low-frequency modulation and the result is stable andrelatively free of noise. Next, the light so modulated is passed throughthe second modulator M₂, which adds additional, again preferablysinusoidal, modulation with a period Δλ₂ different from the period Δλ₁of the first modulator. This modulation period is chosen such that thefringes are localized and rendered visible at a distance significantlylarger than in the case produced by the first modulation. This twicemodulated light is then injected into the common-path interferometer Iand SCI is practiced in conventional manner as taught in the relevantpatents referenced above.

The preferred modulation is sinusoidal because of its relativesimplicity of implementation. Accordingly, the invention is described interms of sinusoidal modulation; however, any modulation as a function offrequency that could be implemented to produce a desired fringe patternwould be acceptable to practice the invention. Similarly, the secondmodulator of the invention can be implemented conveniently with thedelay line present in a conventional Michelson interferometer.Therefore, the invention is described in terms of such a delay line, butit should not be understood to be so limited. For convenience, aschematic representation of the Michelson configuration is shown in FIG.2. The same can be said for the common-path configuration interferometerused to carry out SCI with an extended range according to the invention,which is described in terms of the preferred Fizeau configuration butcould as well be implemented with other interferometers.

Referring to FIG. 2, the incoming Input light is divided by the beamsplitter BS into separate beams that travel respective separate anddifferent distances L₁ and L₂. After reflection from respective mirrorsR₁ and R₂ along their separate paths, the beams are recombined at thebeam splitter BS, and the spectrum of the resulting Output light isgoing to be modulated sinusoidally. As is well understood in the art,the period of modulation can be changed simply by adjusting the opticalpath difference ΔL=2 (L₁−L₂), thereby providing an effective, easilyimplemented, and extremely convenient mechanism for changing themeasurement range of the downstream interferometer for practicing SCI.

In general terms, the function of the modulator M₁ is to control thespectrum of the light emitted by the source S so as to produce fringesat a short distance from the reference surface. This can be achievedeasily by using conventional spectrum filtering methods, such as agrating or any method described in the art. As described in U.S. Pat.No. 8,422,026, this modulator also needs to have the capability ofchanging the phase of the spectral modulation in order to allow the SCIimplementation of any previously described fringe analysis methods, suchas phase shifting and heterodyne detection (see U.S. Pat. No.9,618,320). The function of the second modulator M2 is to apply thesecond sinusoidal spectral modulation to the interferometric beam suchthat fringes can be formed at significant and adjustable distances fromthe reference surface. As explained above, the use of the delay line ofan unbalanced Michelson interferometer produces an Output light that issinusoidally modulated. The period of modulation corresponds to thedownstream location of formation of fringes at a distance from thereference mirror of the Fizeau interferometer I (FIG. 1) that is exactlyequal to the difference in the optical paths of the arms of theMichelson delay line. This delay can be easily adjusted by changing thelength of one of the arms and can reach measurement ranges in the orderof several meters.

In summary, by using two modulators it is possible to produce a lightbeam with a spectrum reflecting the superposition of two sinusoidalmodulations, one with a relatively coarse period Δλ₁, produced by aspectrally controllable light source, and the other with small periodΔλ₂ produced by a delay line. As mentioned, the modulator M₁ also hasthe capability of manipulating the phase of the output signal.Accordingly, the combined spectral modulation of the beam received fromthe source S results in a multiplication of two sinusoidal modulationsof the original spectrum, with an intensity distribution that can becalculated by the equation

$\begin{matrix}{{{I(\lambda)} = {{I_{S}(\lambda)}( {1 + {A_{1}{\sin ( {{2\pi \frac{\lambda}{{\Delta\lambda}_{1}}} + \varphi} )}}} )( {1 + {A_{2}{\sin ( {2\pi \frac{\lambda}{{\Delta\lambda}_{2}}} )}}} )}},} & (2)\end{matrix}$

where I_(S)(λ) is the intensity of the source light, φ is the phaseshift of the spectral modulation controlled by the modulator M₁, and A₁and A₂ are the contrasts of modulation produced by modulator M₁ and M₂,respectively.

As disclosed and demonstrated in U.S. Pat. No. 8,422,026, Fourieranalysis can be applied to predict where fringes are going to be visiblein the measurement space of the interferometric system. Using theconvolution theorem of Fourier analysis, the resulting function is aconvolution of the functions describing the distribution of fringecontrast C for the individual modulations M₁ and M₂, denoted as F₁ andF₂; i.e., the resulting intensity distribution will be a convolution ofthe intensity distributions attributable to the original source whenmodulated separately by each sinusoidal signal. FIG. 3 illustrates suchdistributions of fringe contrast for a source modulated separately onlyby M₁, by M₂, and then by the combination of M₁ and M₂. The top graphshows the locations along the distance axis L of the fringe contrastvisibility C for a spectral source with a single sinusoidal modulationwith low-frequency period Δλ₁. The 0 distance indicates the location ofthe reference surface. As seen in the top graph, there are twolocations, P₊₁ and P⁻¹, where the fringes are going to be visible withpeaks P. The peak with a positive index is located in front of thereference surface and the peak with a negative index is located behindthe reference surface (corresponding to negative values of L).Similarly, the source modulated by M₂ alone (middle graph) produces peaklocations P₊₂ and P⁻² that are significantly further away from thereference surface because of the much smaller period of modulation Δλ₂produced by the delay line. The fringe locations for the combinedmodulation M₁*M₂ of the source light are shown in the bottom graph ofthe figure and are the result of convolution of the intensity functionsthat produced the first and second graphs. In addition to the previouslyidentified peaks, fringes are also visibly present at new locationsoffset from the original locations resulting from modulation M₂ (seen aspeaks P₊₂ and P⁻²). These offsets correspond to the distance of fringelocation produced by modulation M₁ on the source light in both positiveand negative L directions. They are denoted as P⁻²⁻¹, P⁻²⁺¹ for negativevalues of L and P⁺²⁻¹, P₊₂₊₁ for positive values of L. The first indexindicates the location of the peak resulting from modulation M₂ and thesecond index shows the offset due to M₁. Inasmuch as the modulation M₁produced by the first modulator has the capability of phase shifting,the fringes located at these new locations will have the same capabilityas well. Therefore, they can be used without mechanical shifting of thesample to analyze fringe patterns formed at these locations. It shouldbe noted that the maximum contrast of fringes at all locationsidentified by two indices is reduced to 0.25, which is less thantraditionally considered necessary for optimal fringe analysis. However,the recent availability of new, higher resolution cameras has renderedinconsequential this reduction in contrast.

It is also worth noting that the implementation of modulator M₂ can beachieved simply with a delay line such as that of a Michelsoninterferometer because M₂ does not require the ability to control thephase of the spectral modulation. The function of M₂ is only tointroduce very short-period modulations into the spectrum. The functionof fringe phase control can instead be allocated entirely to modulatorM₁, which, contrary to M₂, needs to support only modest period spectrummodulations. Thus, in practice, it is possible to perform courseadjustment of the fringe location using the modulator M₂ and fine tunethe contrast of the fringes by adjusting the period of M₁. That is, thelocation of fringes is easily obtained by changing the ΔL in the delayline; once the fringes are identified, their precise location can befine-tuned with M₁.

FIG. 4 illustrates the preferred combination of components of aninterferometric system configured to practice SCI with an extended rangeaccording to the invention. A Fizeau interferometer 10 is used becauseof its common-path reference and object arms and the related advantages.The input beam L to the interferometer is reflected by a beam splitter12 toward a reference surface R and an object surface O, from whererespective reflected beams Lr and Lo travel in common path through thesplitter 12, interfere, and are detected by a detector 14. Asillustrated schematically in the figure, a spectrally controllable lightsource 16 (which in now conventional SCI practice can be implemented bythe combination of a broadband source S with a first spectral modulatorM₁—see FIG. 1—as taught in U.S. Pat. No. 8,810,884) is coupled to aMichelson interferometric delay line 18 (corresponding to the secondmodulator M₂ of FIG. 1) to produce a twice modulated beam that isinjected into the Fizeau interferometer. The delay between the beams L₁and L₂ reflected by the two mirrors R₁ and R₂, respectively, introducesthe additional sinusoidal modulation required to extend the range ofmeasurement of the Fizeau interferometer. A translating mechanism 20 isused to change the OPD between beams L₁ and L₂, in so doing providing acontrol over the fringe location in the measurement space of theinterferometer. A computer 22 is used in conventional manner to producethe desired modulations in the light emitted by the source 12 and in thedelay line 14 by controlling the translating mechanism 20. The computer16 is also programmed to perform fringe analysis of the localizedfringes produced in the measurement space of the interferometer. Amonitor 24 is normally also provided for operator functionality.

While the invention has been shown and described herein in what isbelieved to be the most practical and preferred embodiments, it isrecognized that departures can be made therefrom within the scope of theinvention. For example, the invention has been illustrated withreference to Fizeau and Michelson interferometers, but the principles ofthis disclosure are equally applicable to any other type of laserinterferometer where white-light scanning could provide advantages.Similarly, the invention has been described in terms of a spectrallycontrollable light source that includes a broadband source and amodulator as separate components because that is the way the inventionhas been implemented to date (on account of the development of thesources described in U.S. Pat. No 8,810,884); however, it is importantto make clear that any single-component spectrally controllable source,such as currently available lasers capable of spectral modulation, wouldbe suitable to practice the invention. Therefore, the term “spectrallycontrollable light source” is intended to mean any light source capableof spectral modulation. Furthermore, the modulation provided by thesecond modulator described above could also result from additionalmodulation provided by the same spectrally controllable source. Inasmuchas the heart of the invention is the recognition that the range of SCIcan be extended by the application of multiple modulations to the lightinjected into the interferometer, those skilled in the art will readilyunderstand that the result of the superposition of multiple modulationswill be the same whether they occur sequentially or contemporaneously(as also indicated by the underlying mathematics). No single spectrallycontrollable source capable of such multiple modulations is known at thepresent time. However, it is likely that such light sources will beavailable in the future because of the demand driven by SCI and the factthat the physical requirements for their implementation are wellunderstood. Therefore, for the purposes of the claims that follow,“spectrally controllable light source” is defined to include any lightsource capable of emitting spectrally modulated light, whether throughsingle or multiple modulation, and whether through sequential orcontemporaneous modulation. Thus, elements S, M₁ and M₂, shown asseparate components in FIG. 1 for clarity of description, for thepurposes of defining the scope of the invention should be considered tobe a spectrally controllable light source, as claimed.

Furthermore, it is also important to underscore the fact that sinusoidalmodulation is much preferred at this time for the reasons given above,but it is not essential to the invention. For example, spectralmodulation could be obtained with an etalon, which would producemultiple visible fringes at each peak defined by the etalon's freespectral range. It is not envisioned that this type of modulation wouldbe useful in the long-period modulation produced by the spectrallycontrollable source, but it could be in the implementation of theshort-period modulation. As such, the measurement range of theinterferometer could be extended to the limit allowed by the etalon'sfinesse and the corresponding loss of contrast. While such exemplaryimplementation is considered impractical at present, it could becomeimportant as the art of SCI continues to be developed. In view of theforegoing, the invention is not to be limited to the disclosed detailsbut is to be accorded the full scope of the claims, including any andall equivalents thereof.

1. An interferometric system for spectrally controlled interferometricmeasurements, comprising: an interferometer with a reference arm, anobject arm, and means for combining reference and object beams toproduce a combined interference beam; and a spectrally controllablelight source capable of spectral modulation of a light beam to generateinterference fringes with a modulation peak at a selected location alongan optical path of the combined interference beam; said light sourcebeing capable of further spectral modulation of the light beam prior toinjection into said interferometer, said selected location beingcontrollable as a function of a modulation period applied to saidfurther spectral modulation.
 2. The interferometric system of claim 1,wherein said interferometer is a common-path interferometer.
 3. Theinterferometric system of claim 2, wherein said common-pathinterferometer is a Fizeau interferometer.
 4. The interferometric systemof claim 1, wherein said spectral modulation is sinusoidal.
 5. Theinterferometric system of claim 1, wherein said further spectralmodulation is sinusoidal.
 6. The interferometric system of claim 5,wherein said sinusoidal further spectral modulation is produced with aninterferometric delay line.
 7. The interferometric system of claim 6,wherein said interferometric delay line is in Michelson configuration.8. An interferometric system for spectrally controlled interferometricmeasurements, comprising: a Fizeau interferometer; a spectrallycontrollable light source capable of sinusoidal spectral modulation togenerate interference fringes with a modulation peak at a selectedlocation along an optical path of an interference beam produced by saidFizeau interferometer; and an interferometric delay line in Michelsonconfiguration adapted to further modulate light emitted by saidspectrally controllable light source prior to injection into said Fizeauinterferometer, said selected location being controllable as a functionof a sinusoidal modulation period applied through said delay line.
 9. Amethod for increasing the measurement range of a spectrally controlledinterferometric system, comprising the following steps: providing aninterferometer with a reference arm, an object arm, and means forcombining reference and object beams to produce a combined interferencebeam; providing a spectrally controllable light source; generating aspectrally modulated beam that produces interference fringes in saidinterferometer with a modulation peak at a selected location along anoptical path of the combined interference beam; and further spectrallymodulating said modulated beam prior to injection into saidinterferometer, said selected location being controllable as a functionof a period of modulation applied during said further spectrallymodulating step.
 10. The method of claim 9, wherein said steps ofgenerating a spectrally modulated beam and further spectrally modulatingthe modulated beam are carried out by applying, respectively, long andshort periods of spectral modulation relative to each other.
 11. Themethod of claim 10, wherein said interferometer is a common-pathinterferometer.
 12. The method of claim 11, wherein said common-pathinterferometer is a Fizeau interferometer.
 13. The method of claim 9,wherein said spectrally modulating step is carried out with sinusoidalmodulation.
 14. The method of claim 9, wherein said further spectrallymodulating step is carried out with sinusoidal modulation.
 15. Themethod of claim 9, wherein said sinusoidal modulation is produced withan interferometric delay line.
 16. The method of claim 15, wherein saidinterferometric delay line is in Michelson configuration.
 17. The methodof claim 9, wherein said interferometer is a Fizeau interferometer, saidstep of generating a modulated beam is carried out with sinusoidalmodulation, said further spectrally modulating step is carried out withsinusoidal modulation by an interferometric delay line in Michelsonconfiguration; and said steps of generating the spectrally modulatedbeam and further spectrally modulating the modulated beam are carriedout by applying, respectively, long and short periods of spectralmodulation relative to each other.